發(fā)布時(shí)間：2018-07-15 19:00

【摘要】：隨著分?jǐn)?shù)階微積分理論的發(fā)展,電氣工程領(lǐng)域涌現(xiàn)出很多分?jǐn)?shù)階模型及應(yīng)用,如變壓器繞組、傳輸線、電纜線路、超級電容器等分?jǐn)?shù)階模型。這些模型不僅降低了模型的復(fù)雜度,而且提高了仿真精度,使仿真結(jié)果更加符合實(shí)際。分?jǐn)?shù)階電路理論是研究這些分?jǐn)?shù)階模型的基礎(chǔ),所以分?jǐn)?shù)階電路元件、分?jǐn)?shù)階電路的性質(zhì)以及分?jǐn)?shù)階電路的仿真計(jì)算研究對于電氣工程的發(fā)展具有重要意義。傳統(tǒng)整數(shù)階電路元件可以用電磁場知識加以描述,分?jǐn)?shù)階電磁場作為傳統(tǒng)電磁場的拓展,也可以很好地解釋分?jǐn)?shù)階電路元件。本文將分?jǐn)?shù)階Maxwell方程進(jìn)行泰勒級數(shù)展開得到各階次Maxwell方程,利用特定階次的電場、磁場組合時(shí)的分?jǐn)?shù)階波阻抗對分?jǐn)?shù)階元件加以描述,從電磁場角度印證了分?jǐn)?shù)階元件的存在。分?jǐn)?shù)階電路的性質(zhì)研究是分?jǐn)?shù)階電路理論發(fā)展的基礎(chǔ),分?jǐn)?shù)階微積分的引入使電路產(chǎn)生了許多新的性質(zhì)。本文根據(jù)已有研究,歸納總結(jié)了分?jǐn)?shù)階RL_βC_α電路的相關(guān)性質(zhì),并提出和證明了分?jǐn)?shù)階電路的振蕩條件,為分?jǐn)?shù)階電路理論的發(fā)展奠定了基礎(chǔ)。分?jǐn)?shù)階電路性質(zhì)研究離不開分?jǐn)?shù)階電路的仿真計(jì)算,本文選取L1插值離散逼近法建立了分?jǐn)?shù)階元件的伴生模型,基于MATLAB語言采用稀疏表格法編寫分?jǐn)?shù)階電路分析程序。通過仿真計(jì)算驗(yàn)證了分?jǐn)?shù)階元件伴生模型和仿真程序的正確性。為分?jǐn)?shù)階電路的計(jì)算機(jī)輔助分析提供了有效的輔助工具,一定程度上彌補(bǔ)了當(dāng)前電路分析軟件的不足。
[Abstract]:With the development of fractional calculus theory, many fractional order models and applications have emerged in the field of electrical engineering, such as transformer windings, transmission lines, cable lines, supercapacitors and other fractional order models. These models not only reduce the complexity of the models, but also improve the accuracy of simulation, and make the simulation results more realistic. The theory of fractional circuit is the basis of studying these fractional order models. Therefore, the study of fractional circuit elements, properties of fractional order circuits and simulation of fractional order circuits is of great significance for the development of electrical engineering. Traditional integral order circuit elements can be described by electromagnetic field knowledge, fractional order electromagnetic field as an extension of the traditional electromagnetic field, but also a good explanation of fractional circuit elements. In this paper, the fractional Maxwell equation is expanded by Taylor series to obtain the Maxwell equation of each order. The fractional order element is described by the fractional wave impedance when the electric field and magnetic field are combined, and the existence of the fractional order element is confirmed from the point of view of electromagnetic field. The study of the properties of fractional order circuits is the basis of the development of fractional order circuits. The introduction of fractional calculus makes the circuit produce many new properties. In this paper, the related properties of fractional order RL尾 C偽 circuits are summarized, and the oscillation conditions of fractional order circuits are proposed and proved, which lays a foundation for the development of fractional order circuit theory. The properties of fractional circuit can not be studied without the simulation of fractional circuit. In this paper, we select L1 interpolation discrete approximation method to establish the associated model of fractional component, and use sparse table method to compile the program of fractional order circuit analysis based on MATLAB. The simulation results verify the correctness of the fractional component companion model and the simulation program. It provides an effective assistant tool for the computer aided analysis of fractional circuit, and to some extent makes up for the deficiency of the current circuit analysis software.
【學(xué)位授予單位】：華北電力大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TM13

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本文編號：2125081